 Conditional spin measurement of identical fermions

A measurement addressing a spatial mode can prepare an opposite-spin product in the mode description without violating fermionic antisymmetry. For orthogonal orbitals ${\varphi }_a,{\varphi }_b$, the conditional mode state with spin up in $a$ and spin down in $b$ corresponds to the antisymmetric particle-coordinate state $[{\varphi }_a(1){\varphi }_b(2)|\uparrow \downarrow ⟩-{\varphi }_b(1){\varphi }_a(2)|\downarrow \uparrow ⟩]/\sqrt{2}$. Exchange of mode spin factors is different from full exchange of the identical particles. Only the latter must remain antisymmetric.